Dynamic constraint and variable aggregation in column generation

Hocine Bouarab, Issmail El Hallaoui, Abdelmoutalib Metrane and François Soumis

European Journal of Operational Research, 2017, vol. 262, issue 3, 835-850

Abstract: Starting from the improved primal simplex (IPS) decomposition, introduced by Elhallaoui et al. (2011) to tackle degeneracy in general linear programs, we introduce and discuss the mathematical foundations of improved column-generation decompositions (ICG) that are better than the standard column-generation decomposition when degeneracy is an issue. We also present an improved dynamic constraint aggregation (IDCA), which is a specialization of ICG to efficiently solve set partitioning problems. We show that IDCA improves the dynamic constraint aggregation (DCA) and the multiphase dynamic constraint aggregation (MPDCA) algorithms (Elhallaoui et al., 2005, 2010) that not only reduce degeneracy but also profit from it to efficiently solve set partitioning problems. IDCA solves at each iteration a complementary problem (CP) to obtain a group of variables that can be aggregated or pivoted into the basis to bypass degenerate pivots and decrease the objective value and to obtain more “central” dual solutions to generate new columns. Our numerical results show reduction factors in the solution times exceeding 10 for IDCA compared to a state-of-the-art standard column-generation solver.

Keywords: Large scale optimization; Column generation; Degeneracy; Dynamic constraint aggregation; Improved primal simplex; Set partitioning problems (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037722171730396X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:262:y:2017:i:3:p:835-850

DOI: 10.1016/j.ejor.2017.04.049

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().